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A hyperelliptic curve is a particular kind of algebraic curve.
There exist hyperelliptic curves of every genus . If the genus of a hyperelliptic curve equals 1, we simply call the curve an elliptic curve. Hence we can see hyperelliptic curves as generalizations of elliptic curves. There is a well-known group structure on the set of points lying on an elliptic curve over some field , which we can describe geometrically with chords and tangents. Generalizing this group structure to the hyperelliptic case is not straightforward. We cannot define the same group law on the set of points lying on a hyperelliptic curve, instead a group structure can be defined on the so-called Jacobian of a hyperelliptic curve. The computations differ depending on the number of points at infinity. Imaginary hyperelliptic curves are hyperelliptic curves with exactly 1 point at infinity: real hyperelliptic curves have two points at infinity.
and 8 Related for: Imaginary hyperelliptic curve information
hyperellipticcurve. The computations differ depending on the number of points at infinity. Imaginaryhyperellipticcurves are hyperellipticcurves with...
to 2g + 1, the curve is called an imaginaryhyperellipticcurve. Meanwhile, a curve of degree 2g + 2 is termed a real hyperellipticcurve. This statement...
just as we use the group of points on an elliptic curve in ECC. An (imaginary) hyperellipticcurve of genus g {\displaystyle g} over a field K {\displaystyle...
there are two types of hyperellipticcurves, a class of algebraic curves: real hyperellipticcurves and imaginaryhyperellipticcurves which differ by the...
(an abelian surface): what would now be called the Jacobian of a hyperellipticcurve of genus 2. After Abel and Jacobi, some of the most important contributors...
1, and the numerator is a quadratic. As an example, consider the hyperellipticcurve C : y 2 + y = x 5 , {\displaystyle C:y^{2}+y=x^{5},} which is of...
- includes examples Explicit calculation of period matrices for hyperellipticcurves - includes examples Algorithm for computing periods of hypersurfaces...
in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with...
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